Human-associated microbial communities have been implicated in a variety of chronic diseases, including inflammatory bowel diseases, obesity, and autoimmune disorders like diabetes. Environmental communities are also important for bioconversion of waste products in biofuel production. However, microbiomes are highly complex systems involving mutualism and competition between many constituent organisms, and a variety of fundamental and interesting computational challenges remain in the modeling of pathogenicity and community-wide response to perturbations. In this talk I will discuss several computational and statistical approaches to predictive modeling of microbiome behavior using high-throughput metagenomic and transcriptomic sequencing data, including models that leverage biological structures such as phylogenies and gene ontologies to extract features and constrain model complexity.